If `A(3,4),B(7,12)` and `P(x,x)` are such that `(PA)^(2)>(PB)^(2)>(AB)^(2)` ,Then the integral value of `x` can be

A(1,2),B(2,- 3),C(-2,3) are 3 points. A point P moves such that PA^(2)+PB^(2)=2PC^(2) . Show that the equation to the locus of P is 7 x - 7y + 4 = 0 .

Let p = 144 ^(sin^(2)x) + 144^( cos^(2)x), then the number of integral values of such p's can take are

"If "-(2)/(7),x,-(7)/(2)" are in G.P. Find the value of x."

A(2,3) , B (1,5), C(-1,2) are the three points . If P is a point such that PA^(2)+PB^(2)=2PC^2 , then find locus of P.

If 4x+3y-12=0 touches (x-p)^(2)+(y-p)^(2)=p^(2) , then the sum of all the possible values of p is

If A(-3,4) ,B(5,6),then find point P on x-axis such that PA+PB is Minimum.

If x in R then (x^(2)+2x+a)/(x^(2)+4x+3a) can take all real values if

Suppose A, B are two points on 2x-y+3=0 and P(1,2) is such that PA=PB. Then the mid point of AB is

If f(x)=(x^(2)+3x+2)(x^(2)-7x+a) and g(x)=(x^(2)-x-12)(x^(2)+5x+b) , then the value of a and b , if (x+1)(x-4) is H.C.F. of f(x) and g(x) is (a) a=10 : b=6 (b) a=4 : b=12 (c) a=12 : b=4 (d) a=6 : b=10

Consider a circle , in which a point P is lying inside the circle such that (PA)(PB)=(PC)(PD) ( as shown in figure ) . On the basis of above information , answer the questions If log_(PA) x=2 , log_(PB)x=3, log_(x) PC=4 , then log_(PD) x is equal to